Consider a sequence of independent trials, with each trial being a success with probability p. Given that the kth success occurs on trial n, show that all possible outcomes of the first n − 1 trials that consist of k − 1 successes and n − k failures are equally likely.
Answer to relevant QuestionsIf X and Y are independent binomial random variables with identical parameters n and p, show analytically that the conditional distribution of X given that X + Y = m is the hypergeometric distribution. Also, give a second ...Let U denote a random variable uniformly distributed over (0, 1). Compute the conditional distribution of U given that (a) U > a; (b) U < a; where 0 < a < 1. Establish Equation (6.2) by differentiating Equation (6.4). (a) If X has a gamma distribution with parameters (t, λ), what is the distribution of cX, c > 0? (b) Show that has a gamma distribution with parameters n, λ when n is a positive integer and χ22n is a chi-squared random ...Show how to compute Cov(X, Y) from the joint moment generating function of X and Y.
Post your question